The Starobinsky model of inflation is obtained by adding to the Einstein action a quadratic in the scalar curvature term. This can be linearised by introducing a Lagrange multiplier which becomes, in the Einstein frame, an ordinary scalar field (the so-called scalaron) with a particular potential [1]} that can drive inflation compatible with present cosmological observations.
Since the scalar curvature belongs in supergravity to a chiral multiplet [2]}, the supersymmetric extension of \(R^2\)  must be written as a D-term, which needs two superfield-Lagrange multipliers to be linearised [3]}. One of them contains the inflaton, while the other is the goldstino superfield that breaks supersymmetry. The model is described by a no-scale type supergravity with a Kähler potential \(K\)  and a superpotential \(W\)  given by:
\(K=-3\ln \left(T+{\bar{T}} - C{\bar{C}}\right)\quad ;\quad W=\mu C(T-{k})\,,\) 
